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Arakawa, Suzuki and Tsuchiya constructed a correspondence between certainmodules of the trigonometric Cherednik algebra $\mathfrak{C}_N$ depending on aparameter $\kappa\in\mathbb{C}$, and certain modules of the affine Lie algebra$\widehat{\mathfrak{sl}}_m$ of level $\kappa-m$. We give a detailed proof ofthis correspondence by working with the affine Lie algebra$\widehat{\mathfrak{gl}}_m$ alongside of $\widehat{\mathfrak{sl}}_m$. We alsorelate this construction to a correspondence between certain modules of thedegenerate affine Hecke algebra $\mathfrak{H}_N$ and all modules of$\mathfrak{sl}_m$ or $\mathfrak{gl}_m$. The latter correspondence wasconstructed earlier by Cherednik.

On the functor of Arakawa, Suzuki and Tsuchiya